login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A211858 Number of partitions of n into parts <= 3 with the property that all parts have distinct multiplicities. 8
1, 1, 2, 2, 3, 4, 5, 7, 7, 8, 10, 14, 12, 19, 19, 19, 23, 30, 26, 37, 35, 37, 43, 52, 45, 60, 59, 61, 68, 80, 70, 90, 88, 91, 100, 113, 101, 126, 124, 127, 136, 153, 139, 168, 165, 168, 180, 199, 182, 216, 212, 216, 229, 251, 232, 269, 265, 270, 285, 309, 286 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..500

Doron Zeilberger, Using generatingfunctionology to enumerate distinct-multiplicity partitions.

FORMULA

G.f.: -(2*x^17 +3*x^16 +5*x^15 +5*x^14 +4*x^13 +2*x^11 +2*x^9 +3*x^8 +5*x^7 +5*x^6 +6*x^5 +6*x^4 +5*x^3 +4*x^2 +2*x+1) / ((x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^2+1) *(x+1)^2 *(x^2+x+1)^2 *(x-1)^3). - Alois P. Heinz, Apr 26 2012

EXAMPLE

For n=3 the a(3)=2 partitions are {3} and {1,1,1}. Note that {2,1} does not count, as 1 and 2 appear with the same nonzero multiplicity.

PROG

(Haskell)

a211858 n = p 0 [] [1..3] n where

   p m ms _      0 = if m `elem` ms then 0 else 1

   p _ _  []     _ = 0

   p m ms ks'@(k:ks) x

     | x < k       = 0

     | m == 0      = p 1 ms ks' (x - k) + p 0 ms ks x

     | m `elem` ms = p (m + 1) ms ks' (x - k)

     | otherwise   = p (m + 1) ms ks' (x - k) + p 0 (m : ms) ks x

-- Reinhard Zumkeller, Dec 27 2012

CROSSREFS

Cf. A001399, A098859.

Cf. A105637, A211859, A211860, A211861, A211862, A211863.

Sequence in context: A082543 A050322 A325512 * A029012 A095699 A112192

Adjacent sequences:  A211855 A211856 A211857 * A211859 A211860 A211861

KEYWORD

nonn,easy

AUTHOR

Matthew C. Russell, Apr 25 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 25 12:55 EDT 2019. Contains 324352 sequences. (Running on oeis4.)